Why Do Nonlinear Finite Element Analysis?

In this book we aim to provide some background information about
the principles of the finite element technique as applied to
nonlinear problems. The benefits of using nonlinear finite element
analysis are highlighted, and some general guidelines are given for
efficient use of the technique. The term FE will be used throughout
the booklet to mean finite element.

The book is aimed at decision-makers; those practicing engineers
and managers who may influence the design process within their
organization. The objective of the booklet is to demonstrate to the
engineers, in a clear and practical manner, he reasons why their
organizations should be using nonlinear FE analysis.

The decision to use any tool or process should be driven by
commercial factors. A company should consider the use of any
available tools that may reduce its development costs, reduce its
lead times, enable it to develop products that are better than
those produced by its competitors, or enable it to manufacture
products using less material and less complex or costly processes.

In many cases the use of nonlinear finite element analysis can
provide these kind of benefits. It is perhaps appropriate,
therefore, that engineers should consider whether they can afford not
to use nonlinear FE analysis.

There are, of course, some negative aspects to this issue: any
prospective user of nonlinear finite elements should consider the
additional costs of the software and the computer on which to run
it, the costs associated with training staff, and the additional
work required to generate the material and structural data that a
good analysis demands. In this booklet we endeavour to provide a
balanced view of the benefits and costs of using nonlinear FE
analysis.

Let us return to the key question – why use nonlinear FE
analysis?

All physical structures exhibit nonlinear behaviour to some extent.
They may be made of rubber or plastic materials that do not have a
constant modulus, they may be operating over a range of
temperatures where the material behaviour at high temperature is
very different th that at ambient, or they may be made up of
components that contact each other. In such cases linear FE
analysis is, as we will see, an approximation that makes the
analysis of structures more tractable. However, the assumptions of
linearity are often not adequate for real structures. If a
nonlinear FE method is used, many of these limiting assumptions are
no longer required; therefore, the analysis of a structure
undergoing some form of nonlinear behaviour may be much more
accurate if a nonlinear FE analysis is carried out.

It is important to note that both nonlinear FE analyses should
provide the same answer for a linear problem. It is only when the
problem contains some form of nonlinearity that the linear
assumptions lead to a loss of accuracy.

The ability to predict accurately the response of a structure to a
given loading allows engineers to improve their knowledge of the
structure and to increase their confidence in their understanding
of the structure’s behaviour. Ultimately, more accurate
analysis enables engineers to improve their products.